Illustration of our model of umbral oscillations inherited from subphotospheric fast-body modes. The yellow area represents the high-β region (c_s > v_A) below the sunspot surface, and the white area represents the low-β region (c_s < v_A). The black solid line between the two regions represents the equipartition layer (c_s = v_A) where the mode conversion can occur. The gray vertical lines illustrate the magnetic field lines of the flux tube, and the vertical dashed line indicates the boundary of the flux tube. The red line demonstrates the vertical velocity v_z of fast body waves, and the blue line represents v_z of converted slow waves. The dash-dotted horizontal line represents the detection layer of the chromosphere. The two panels in the bottom right corner show the vertical velocity fluctuation of two azimuthal modes of m = 0 and 2. The top right panel shows a horizontal cross-section view of the modeled oscillation patterns.